最小二乘法与反问题误差最优模的选择  

THE LEAST SQUARE METHOD AND THE CHOICE OF RESIDUALS′ OPTIMUM NORMAL FOR INVERSE PROBLEMS

作　　者：张文生[1] 何樵登[1] 

机构地区：[1]长春地质学院地球物理系

出　　处：《长春地质学院学报》1996年第4期454-460,共7页

基　　金：国家自然科学基金委员会;中国科学院;中国石油天然气总公司和大庆石油管理局联合资助

摘　　要：指出了（阻尼）最小二乘法能够成功解决反问题的本质，然而它并不总是最优准则。如果误差服从拉普拉斯分布，那么最小绝对值准则最优，如果误差近似均匀分布，则应选极小极大准则。首次提出的两个准则可一般地评价或选择最优模，最优模使后验概率取极大值或使某种差值取极小值。Based on the least square criterion, the least souares method is a commonly used method for inverse problems. At first, we discussed the essence of its success in sloving inverse problems. Then, we considered the method as not always successful one and give some general results of choosing residuals′ normal, and proposed two criteria to measure the performance of residuals′ normal. Finally, the numerical calculation proves the theory results powerly. All conclusions are clear and significant for sloving inverse problems.

关 键 词：最小二乘法 误差模型 反问题 地震勘探 

分 类 号：P631.4[天文地球—地质矿产勘探] O241.1[天文地球—地质学]